Is it better to use regular or premium processing for the EB-1A visa process in terms of success rate? Also does Premium Processing apply for just the EB-1A or both the EB-1A and adjustment of status. 

Well there is no proof but there is a practical concern that adjudicating officers may be more prone to issue requests for evidence under premium processing. This reason is that they are under a time constraint to issue a response in 15 business days and it sometimes might be easier to issue a request for evidence to buy more time to respond. 

On the underhand, ultimately premium processing is preferred because it gives more of an opportunity to be meticulous in writing the original petition and the EB-1A athlete or coach will find out sooner than later if USCIS is going to be tough on the petition.